Rényi and Ulam came up independently with the version where the Responder may lie during the game at most \(\ell \)  times. Let us denote the minimal number of queries needed for the Questioner in the worst case by \(RU_\ell (n)\) . We have already mentioned that \(RU_0(n)=\lceil \log _2 n\rceil \) . Beside that, the exact value of \(RU_\ell (n)\)  is known for all \(n\)  when \(\ell =1,2,3\) . Furthermore, for all \(\ell \)  there exist a lower and an upper bound which differ by at most \(\ell \) . For more details see [1]}, [2]}.
